It is well known that the laminated formation rock presents anisotropic mechanical properties. This anisotropic behavior is due to formation's sedimentary structures, such as the fine layers, oriented fissures/fractures, or anisotropy fibers/grains. The effects of this anisotropy on seismic shear anisotropy have been well documented since the 1970's, e.g. “Weak Elastic Anisotropy” by Leon Thomsen (Geophysics, Vol. 51, 1986). One common form of the anisotropy model, the Transversely Isotropic (TI) model, has been widely used in geophysical and geomechanical applications, e.g. “A model for bedding related formation failure” by Atkinson, C. and Bradford, 2001 (I.D.R.: OFSR/RN/2001/005/RDV/C). However, one of the major difficulties constraining the applications of the anisotropy model is how to determine the elastic constants from seismic or borehole sonic measurements. This constraint effects even the simplest anisotropy models, such as the TI model, with five independent elastic constants.
Recently, with the development of measuring tools, the borehole's four velocities (a compressional velocity VP, a tube wave velocity VT, a shear horizontal wave velocity VSH, and a shear vertical wave velocity VSV) can be measured with more accuracy, for example, via Schlumberger's new sonic tool SONIC SCANNER. However, it is still impossible to determine the TI properties directly from the measured four velocities.